A335743 Keep the first two digits of a(n) and insert a dot between them; this is now the arithmetic mean (truncated after the first decimal) of the digits used so far in the sequence. Lexicographically earliest sequence of distinct positive terms with this property.

45, 30, 38, 301, 306, 307, 305, 308, 304, 318, 303, 309, 316, 302, 2900, 2901, 2910, 3019, 3009, 3018, 3027, 3028, 3008, 3029, 3007, 3036, 3037, 3017, 3038, 3016, 3039, 3006, 3045, 3046, 3026, 3047, 3025, 3048, 3015, 3049, 3005, 3054, 3055, 3035, 3056, 3034, 3057, 3024, 3058, 3014, 3059, 3004, 3063

Offset: 1

Author

Eric Angelini and Carole Dubois, Jul 02 2020

Keywords

• base
• nonn

Comments

The sequence starts with a(1) = 45 as any a(1) < 45 would not produce an infinite sequence.

Examples

			a(1) = 45; inserting a dot between the first two digits produces 4.5; this is now the arithmetic mean (AM) of the digits used so far in the sequence as (4 + 5)/2 = 9/2 = 4.5 (and 4.5 is 45 with a dot);
a(2) = 30; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far in the sequence as (4 + 5 + 3 + 0)/4 = 12/4 = 3 (and 3 is 30 with a dot);
a(3) = 38; inserting a dot between the first two digits produces 3.8; this is the AM of the digits used so far (when truncated after the first decimal) as (4 + 5 + 3 + 0 + 3 + 8)/6 = 23/6 = 3.83333... which produces 38, and 3.8 is 38 with a dot);
a(4) = 301; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far as (4 + 5 + 3 + 0 + 3 + 8 + 3 + 0 + 1)/9 = 27/9 = 3 [and 3 is 30 with a dot, this 30 being formed by the first two digits of a(4)];
a(5) = 306; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far as (4 + 5 + 3 + 0 + 3 + 8 + 3 + 0 + 1 + 3 + 0 + 6)/12 = 36/12 = 3 (and 3 is 30 with a dot, this 30 being formed by the first two digits of a(5)]);
a(6) = 307; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far (truncated after the first decimal) as (4 + 5 + 3 + 0 + 3 + 8 + 3 + 0 + 1 + 3 + 0 + 6 + 3 + 0 + 7)/15 = 46/15 = 3.0666... which produces 30, this 30 being formed by the first two digits of a(6)]; etc.
		

Crossrefs

Cf. A061383 (arithmetic mean of digits is an integer).